Spin and pseudospin towers of the Hubbard model on a bipartite lattice

In 1989, Lieb proved two theorems about the Hubbard model. One showed that the ground state of the attractive model was a spin singlet state ($S=0$), was unique, and was positive definite. The other showed that the ground state of the repulsive model on a bipartite lattice at half-filling has a total spin given by $|(N_A-N_B)/2|$, corresponding to the difference of the number of lattice sites on the two sublattices divided by two. In the mid to late 1990's, Shen extended these proofs to show that the pseudospin of the attractive model was minimal until the electron number equaled $2N_A$ where it became fixed at $J=|(N_A-N_B)/2|$ until the filling became $2N_B$, where it became minimal again. In addition, Shen showed that a spin tower exists for the spin eigenstates for the half-filled case on a bipartite lattice. The spin tower says the minimal energy state with spin $S$ is higher in energy than the minimal energy state with spin $S-1$ until we reach the ground-state spin given above. One long standing conjecture about this model remains, namely does the attractive model have such a spin tower for all fillings, which would then imply that the repulsive model has minimal pseudopsin in its ground state. While we do not prove this last conjecture, we provide a quick review of this previous work, provide a constructive proof of the pseudospin of the attractive model ground state, and describe the challenges with proving the remaining open conjecture.Comment: (15 pages, to appear in Int. J.Mod. Phys. B

Creation of Favourable Conditions for Introducing Hydrogen Fuel in Russia

The paper presents the key problems that hinder the introduction of new fuel for Russian automobile manufacturers. By analyzing the energy market, as well as trends and forecasts of crude oil and petroleum product prices, it proposes the necessary steps for the Government, along with oil producers and automakers, to gradually convert motor vehicles to hydrogen fuel and, therefore, to occupy a high-potential niche in the energy market. The recommended steps are assumed to be applicable not only to this specific case - introduction of hydrogen to the Russian market - but also to any other alternative fuel in a country with the similar or superior national economy

Effect of plasma suppression additives on electrodynamic characteristics of the torch discharge burning in the air

The paper shows the results of measurements of wave number of electromagnetic wave, which supports burning of high-frequency torch discharge in the mixture of air with water vapor and carbon dioxide. The nonmonotonic dependence of attenuation factor of electromagnetic waves is set on a concentration of water vapor. It is shown that the attenuation degree of electromagnetic field in the plasma with water vapor significantly exceeds the attenuation degree of electromagnetic field in the plasma with carbon dioxide

Soviet industrial production, 1928 to 1955 : real growth and hidden inflation

The mechanism of hidden inflation in Soviet industrial growth statistics between 1928 and 1950 is described. Hidden inflation arose when new products were substituted for old ones. Substitution biases in Soviet and Western growth estimates are compared; the extent of hidden inflation in the Soviet figures is estimated. The view that all Soviet growth series were exaggerated is qualified; the presumption that the lower a figure, the more reliable it must be, is overturned. The Moorsteen paradox, hidden inflation in industry as a whole, but none in machinebuilding where product innovation was most rapid, is explained

Redefining a Blurry Line: A Proposal to Reform the Taxation of Pension Fund Business and Investment Income

Pension funds are established to provide workers in the private and public sectors with tax-advantaged retirement benefits. Corporate and public pension funds today collectively hold portfolios worth trillions of dollars and pursue similar investment strategies designed to balance the requirement of diversification with the need to achieve sufficient investment returns to meet the demands of plan participants and their beneficiaries. While all pension funds are generally exempt from taxation under the Code, tax-qualified corporate pension funds are still subject to tax liability on the receipt of active business income under the Unrelated Business Income Tax (UBIT). This rule creates harsh consequences for corporate pension funds when combined with the Code’s particular definition of “business income” in the context of pension fund investment activity. These rules therefore exacerbate the underlying horizontal inequity issues for participants in private and public pension plans. A recent proposal in Congress attempts to resolve this issue by subjecting public pension funds to tax on UBIT income. This Article explores the rationales for taxing pension funds on UBIT income more generally and the extent of the horizontal inequity that exists due to the differing tax treatment of public and private pension funds. This Article concludes that rather than tax public pension funds on UBIT income, Congress should instead reform the UBIT rules to allow corporate pension funds to invest more freely without fearing tax consequences under the UBIT

Totally Nonnegative Tropical Flags and the Totally Nonnegative Flag Dressian

We study the totally nonnegative part of the complete flag variety and of its tropicalization. We show that Lusztig's notion of nonnegative complete flag variety coincides with the flags in the complete flag variety which have nonnegative Pl{\"u}cker coordinates. This mirrors the characterization of the totally nonnegative Grassmannian as those points in the Grassmannian whose Pl{\"u}cker coordinates are all nonnegative. We then study the tropical complete flag variety and complete flag Dressian, which are two tropical versions of the complete flag variety, capturing realizable and abstract flags of tropical linear spaces, respectively. In general, the complete flag Dressian properly contains the tropical complete flag variety. However, we show that the totally nonnegative parts of these spaces coincide.Comment: 46 pages V2: Elaborated on proof of 5.14 and updated reference

Polyhedral and Tropical Geometry of Flag Positroids

A flag positroid of ranks $\boldsymbol{r}:=(r_1<\dots <r_k)$ on $[n]$ is a flag matroid that can be realized by a real $r_k \times n$ matrix $A$ such that the $r_i \times r_i$ minors of $A$ involving rows $1,2,\dots,r_i$ are nonnegative for all $1\leq i \leq k$. In this paper we explore the polyhedral and tropical geometry of flag positroids, particularly when $\boldsymbol{r}:=(a, a+1,\dots,b)$ is a sequence of consecutive numbers. In this case we show that the nonnegative tropical flag variety TrFl$_{\boldsymbol{r},n}^{\geq 0}$ equals the nonnegative flag Dressian FlDr$_{\boldsymbol{r},n}^{\geq 0}$, and that the points $\boldsymbol{\mu} = (\mu_a,\ldots, \mu_b)$ of TrFl$_{\boldsymbol{r},n}^{\geq 0} =$ FlDr$_{\boldsymbol{r},n}^{\geq 0}$ give rise to coherent subdivisions of the flag positroid polytope $P(\underline{\boldsymbol{\mu}})$ into flag positroid polytopes. Our results have applications to Bruhat interval polytopes: for example, we show that a complete flag matroid polytope is a Bruhat interval polytope if and only if its $(\leq 2)$-dimensional faces are Bruhat interval polytopes. Our results also have applications to realizability questions. We define a positively oriented flag matroid to be a sequence of positively oriented matroids $(\chi_1,\dots,\chi_k)$ which is also an oriented flag matroid. We then prove that every positively oriented flag matroid of ranks $\boldsymbol{r}=(a,a+1,\dots,b)$ is realizable.Comment: 40 page

Marine yeast isolation and industrial application

Over the last century, terrestrial yeasts have been widely used in various industries, such as baking, brewing, wine, bioethanol and pharmaceutical protein production. However, only little attention has been given to marine yeasts. Recent research showed that marine yeasts have several unique and promising features over the terrestrial yeasts, for example higher osmosis tolerance, higher special chemical productivity and production of industrial enzymes. These indicate that marine yeasts have great potential to be applied in various industries. This review gathers the most recent techniques used for marine yeast isolation as well as the latest applications of marine yeast in bioethanol, pharmaceutical and enzyme production fields. Keyword

Ультраструктурні зміни кортикотропних клітин передньої частки аденогіпофіза за умов дії червоного шламу та засобів їх корекції

New data concerning the character and the dynamic of the ultrastructural changes of adenohypophysis corticotrophic cells under the prolonged influence of the red mud to the body has been received with the help of modern methods (electronic microscopy, optical Image Analysis morphometry). The correction method of the red mud influence on the corticotrops with the alpha-tocopherol exploitation has been suggested. It has been established that rats staying under the red mud influence during 14 days leads to the intensification of the corticotrophic cells function, which is accompanied by the increasing of chromatin in the corticotrophic nuclei of middle area, by the increasing of mitochondria in cytoplasm, secretory granules and their activity index, in the comparison with the test animals. However, it is observed the signs of dystrophic changes in individual corticotrophic cells, the destructive reconstructions in the nucleus structures (hyperchromic, bullate and edema nuclei) and in the membrane cytoplasm structures (endoplasmic reticulum vacuolization with the partial destruction of its membranes and hollow formation, mitochondrial matrix hardening). Ultrastructural changes of corticotrophic cells on 45-days experimental rats point out the evidence of weakening function, which occurs against the background of decrease of chromatin, mitochondria, secretory granules quantity. Expressed dystrophic changes and destructive rebuildings determine in the ultrastructural corticotrophic organization both in the nucleus structures and in the cytoplasm cell membranes and in the endothelium hemocapillar bed, which surround these cells. Ultra structural rebuildings of corticotrophic cells on 180-days experimental rats under the prolonged influence of the red mud are evidence of the suppression continuation of their functions, which are accompanied by destructively dystrophic changes in their structure and conform to the stage of exhaustion general adaptation syndrome. Нerewith, ultrastructural signs of mild activation of intracellular reparative regeneration are determined among certain corticotrophic cells (size and number increasing of the Golgi complex elements and granular endoplasmic reticulum, increasing the number of young forms of mitochondria, free ribosome and polyribosome). Alpha-tocopherol usage under the influence of red mud contributes to the weakening of its toxic effect and force of the stress response of the corticotrophic cells which acquires the expressiveness with the age and the maturity of the animals and the term of alpha-tocopherol influence. There are the normalization marks in the ultrastructural organization of corticotrophic cells indicating a positive alpha-tocopherol impact on the recovery of the corticotrophic cells ultrastructures.Отримано нові дані відносно характеру й динаміки ультраструктурних змін у кортикотропних клітинах аденогіпофіза за умов тривалої дії на організм червоного шламу. Установлено залежність змін структури й функції кортикотропів від тривалості дії червоного шламу у тварин різного віку. Запропоновано спосіб корекції дії червоного шламу на кортикотропи з використанням альфа-токоферолу